In this task, you will be presented with a context from an academic paper and a question separated with a 
. You have to answer the question based on the context.

Q: The split methods (beyond random split) are the following:

Output length: Variation of the setup described by BIBREF2 where the train set consists of examples with output (sparql query or action sequence) length $\le \hspace{-2.5pt} N$, while the test set consists of examples with output length $> \hspace{-2.5pt} N$. For CFQ, we use $N = 7$ constraints. For scan, we use $N = 22$ actions.

Input length: Variation of the above setup, in which the train set consists of examples with input (question or command) length $\le N$, while test set consists of examples with input length $> N$. For CFQ, we use $N=19$ grammar leaves. For SCAN, we use $N=8$ tokens.

Output pattern: Variation of setup described by BIBREF8, in which the split is based on randomly assigning clusters of examples sharing the same output (query or action sequence) pattern. Query patterns are determined by anonymizing entities and properties; action sequence patterns collapse primitive actions and directions.

Input pattern: Variation of the previous setup in which the split is based on randomly assigning clusters of examples sharing the same input (question or command) pattern. Question patterns are determined by anonymizing entity and property names ; command patterns collapse verbs and the interchangeable pairs left/right, around/opposite, twice/thrice. 
 Question: What are other approaches into creating compositional generalization benchmarks?

A: random  Output length Input length Output pattern Input pattern
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Q: We train MaLOPa on the concantenation of training sections of all seven languages. 
 Question: How many languages have this parser been tried on?

A: seven
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Q: Moreover, QA and QG have probabilistic correlation as both tasks relate to the joint probability between $q$ and $a$ . Given a question-answer pair $\langle q, a \rangle $ , the joint probability $P(q, a)$ can be computed in two equivalent ways.

$$P(q, a) = P(a) P(q|a) = P(q)P(a|q)$$ (Eq. 1)

The conditional distribution $P(q|a)$ is exactly the QG model, and the conditional distribution $P(a|q)$ is closely related to the QA model. Existing studies typically learn the QA model and the QG model separately by minimizing their own loss functions, while ignoring the probabilistic correlation between them.

Based on these considerations, we introduce a training framework that exploits the duality of QA and QG to improve both tasks. There might be different ways of exploiting the duality of QA and QG. In this work, we leverage the probabilistic correlation between QA and QG as the regularization term to influence the training process of both tasks. Specifically, the training objective of our framework is to jointly learn the QA model parameterized by $\theta _{qa}$ and the QG model parameterized by $\theta _{qg}$ by minimizing their loss functions subject to the following constraint.

$$P_a(a) P(q|a;\theta _{qg}) = P_q(q)P(a|q;\theta _{qa})$$ (Eq. 3)

$P_a(a)$ and $P_q(q)$ are the language models for answer sentences and question sentences, respectively. Overall, the framework includes three components, namely a QA model, a QG model and a regularization term that reflects the duality of QA and QG. The QA specific objective aims to minimize the loss function $l_{qa}(f_{qa}(a,q;\theta _{qa}), label)$ , where $label$ is 0 or 1 that indicates whether $a$ is the correct answer of $q$ or not. For each correct question-answer pair, the QG specific objective is to minimize the following loss function,

$$l_{qg}(q, a) = -log P_{qg}(q|a;\theta _{qg})$$ (Eq. 6)

where $a$ is the correct answer of $q$ . The third objective is the regularization term which satisfies the probabilistic duality constrains as given in Equation 3 . Specifically, given a correct $\langle q, a \rangle $ pair, we would like to minimize the following loss function,

$$ \nonumber l_{dual}(a,q;\theta _{qa}, \theta _{qg}) &= [logP_a(a) + log P(q|a;\theta _{qg}) \\ & - logP_q(q) - logP(a|q;\theta _{qa})]^2$$ (Eq. 9)

where $P_a(a)$ and $P_q(q)$ are marginal distributions, which could be easily obtained through language model. 
 Question: What does "explicitly leverages their probabilistic correlation to guide the training process of both models" mean?

A:
The framework jointly learns parametrized QA and QG models subject to the constraint in equation 2. In more detail, they minimize QA and QG loss functions, with a third dual loss for regularization.
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